Buy compact, green plants with a healthy root system. Water well and plant out or pot on immediately to avoid checking their growth. Beware of buying zucchini and other half-hardy plants before the risk of frost has passed.
Carefully remove each seedling from its packaging and, holding the root ball rather than the delicate leaves, plant them into prepared soil so that the top of the root ball is just below soil level.
Gently firm the soil around each plant so that it is stable and water well to help it get established. Add a mulch of organic material around each plant (but not touching the stem) to retain soil moisture and suppress weeds.
Label, and add supports for plants that need them as they grow. Cloches are often useful to protect young plants from cold and windy weather. Continue to water the plants regularly until they are established.